Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+6y &= 5 \\ -8x-6y &= -1\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $-6y = 8x-1$ Divide both sides by $-6$ to isolate $y$ $y = {-\dfrac{4}{3}x + \dfrac{1}{6}}$ Substitute this expression for $y$ in the first equation. $4x+6({-\dfrac{4}{3}x + \dfrac{1}{6}}) = 5$ $4x - 8x + 1 = 5$ Simplify by combining terms, then solve for $x$ $-4x + 1 = 5$ $-4x = 4$ $x = -1$ Substitute $-1$ for $x$ back into the top equation. $4( -1)+6y = 5$ $-4+6y = 5$ $6y = 9$ $y = \dfrac{3}{2}$ The solution is $\enspace x = -1, \enspace y = \dfrac{3}{2}$.